{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-1184"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-1184","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"Measures Of Concordance Of Polynomial Type","abstract":"A measure of concordance, $\\kappa$, is of polynomial type if and only if $\\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on $(0,1)^{2n}$ is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in $d_n$. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau.","abstract_html":"A measure of concordance, $\\kappa$, is of polynomial type if and only if $\\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on <span class=\"etd-inline-math\">(0,1)<sup>2n</sup></span> is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in <span class=\"etd-inline-math\">d<sub>n</sub></span>. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in <span class=\"etd-inline-math\">d<sub>2</sub></span> generating Kendall&#x27;s tau. Finally, another family of measures of concordance is given containing those generated by finite measures in <span class=\"etd-inline-math\">d<sub>2</sub></span> as well as Kendall&#x27;s tau.","abstract_has_math":true,"creators":["Edwards, Heather"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Taylor, Michael"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-01-01T08:00:00Z","date_published":"2004-01-01T08:00:00Z","updated_at":"2026-07-24T05:08:16Z","subjects":["measure of concordance","copula","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000254"],"render_values":[{"text":"CFE0000254","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/185","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Taylor, Michael"]},{"key":"dc:creator","label":"Author","values":["Edwards, Heather"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Doctoral Dissertation (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["measure of concordance","copula","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0000254"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/185"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Doctor of Philosophy (Ph.D.)","College of Arts and Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["A measure of concordance, $\\kappa$, is of polynomial type if and only if $\\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on $(0,1)^{2n}$ is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in $d_n$. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Measures Of Concordance Of Polynomial Type"]}]}],"canonical_facts":{"dc:contributor":["Taylor, Michael"],"dc:creator":["Edwards, Heather"],"dc:description":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Doctor of Philosophy (Ph.D.)","College of Arts and Sciences","Mathematics"],"dc:description.abstract":["A measure of concordance, $\\kappa$, is of polynomial type if and only if $\\kappa (tA+(1-t)B)$ is a polynomial in $t$ where $A$ and $B$ are 2-copulas. The degree of such a type of measure of concordance is simply the highest degree of the polynomial associated with $\\kappa$. In previous work [2], [3], properties of measures of concordance preserving convex sums (equivalently measures of concordance of polynomial type degree one) were established; however, a characterization was not made. Here a characterization is made using approximations involving doubly stochastic matrices. Other representations are provided from this characterization leading naturally to two interpretations of degree one measures of concordance. The existence of a family of measures of concordance of polynomial type having higher degree generated by a certain family of Borel measures on $(0,1)^{2n}$ is also shown. The representation of this family immediately leads to a probabilistic interpretation for all finite measures in $d_n$. Also, higher degree analogs of commonly known degree one measures of concordance are given as examples. For the degree 2 case in particular, we see there is no finite measure in $d_2$ generating Kendall's tau. Finally, another family of measures of concordance is given containing those generated by finite measures in $d_2$ as well as Kendall's tau."],"dc:format":["application/pdf"],"dc:identifier":["CFE0000254"],"dc:identifier.uri":["https://stars.library.ucf.edu/etd/185"],"dc:language":["English"],"dc:subject":["measure of concordance","copula","Mathematics"],"dc:title":["Measures Of Concordance Of Polynomial Type"],"dc:type":["Doctoral Dissertation (Open Access)"]},"updated_at":"2026-07-24T05:08:16Z"}